Question: in hw 5.2, the questions states that the angle of elevation to the top of a sand dune is 20degrees, and after walking 800ft closer, he guessed that the angle of elevation had increased by 15degrees.Approximately how tall is the dune?
What I know: I think you make a right triangle in it
What I need to know: where to make your triangle and how to find how tall it is.
You will actually get two triangles here. There are two unknowns, the height of the dune and the distance from the first point to the dune.
The first triangle has an unknown side and an angle of elevation of 20 degrees--that is, the angle between a line along the ground and a line to the top of the dune is 20 deg. The unknown side is the distance along the ground a point directly under the peak of the dune, so this side will be perpendicular to the height of the dune. So the unknown side will be the side adjacent to the 20 degree angle.
If we call the height of the dune h, and the unknown distance x, we therefore have
tan(20 deg) = h / x.
Remember that tan(20 deg) is just a number you can find on your calculator.
The second triangle has angle of elevation 35 deg. A triangle constructed in the same manner as the first will have altitude h and adjacent side x - 800 ft. So
tan(35 deg) = h / (x - 800 ft).
This gives us two equations we can solve for x and h. The easiest way to solve is to solve the first equation for x, then substitute this result in to the second equation. This will give you an equation you can solve for h.